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Question

The sum of three numbers in A.P is 21 and their product is 231. Find the numbers.

A
3,7,11 or 11,7,3
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B
3,6,12 or 12,6,3
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C
3,7,11 or 11,7,3
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D
3,6,12 or 12,6,3
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Solution

The correct option is A 3,7,11 or 11,7,3
Let the numbers be (ad),a,(a+d). Then,
Sum =21(ad)+a+(a+d)=213a=21a=7
Product =231(ad)×a×(a+d)=231
a(a2d2)=231
7(49d2)=231
(49d2)=33
d2=16d=±4
If d=4, then the numbers are 3,7,11. If d=4, then the numbers are 11,7,3
Thus, the numbers are 3,7,11 or 11,7,3.

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